We present a new sticky particle method for the system of pressureless gas dynamics. The method is based on the idea of sticky particles The particle velocities are approximated in a special way using certain reconstruction technique, which leads to reasonable gluing procedure in 2-D case. We show that our particle approximation satisfies the original system of pressureless gas dynamics in a weak sense, but only within a certain residual, which is rigorously estimated. We also explain why the relevant errors should diminish as the total number of particles increases and confirm this by extensive numerical testing.